Related papers: Eilenberg-MacLane spectra as equivariant Thom spec…

We describe the second homotopy group of any CW-complex $K$ by analyzing the universal cover of a locally finite model of $K$ using the notion of $G$-coloring of a partially ordered set. As applications we prove a generalization of the…

We compute the $G$-equivariant homotopy type of the real topological cyclic homology of spherical group rings with anti-involution induced by taking inverses in the group, where $G$ denotes the group $Gal(\mathbb{C}/\mathbb{R})$. The real…

We give a formula for the geometric fixed-points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to…

We describe a general method for algorithmic construction of G-equivariant chain homotopy equivalences from non-equivariant ones. As a consequence, we obtain an algorithm for computing equivariant (co)homology of Eilenberg-MacLane spaces…

Primary cohomology operations, i.e., elements of the Steenrod algebra, are given by homotopy classes of maps between Eilenberg--MacLane spectra. Such maps (before taking homotopy classes) form the topological version of the Steenrod…

The uniform $\mathcal{F}_p$-isomorphism theorem of Quillen gives a comparison map between the Borel equivariant $\mathbf{Z}/p$-cohomology of a space and a limit involving only the Borel equivariant cohomology groups of the same space with…

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…

We prove Eilenberg-Watts Theorem for 2-categories of the representation categories $\C\x\Mod$ of finite tensor categories $\C$. For a consequence we obtain that any autoequivalence of $\C\x\Mod$ is given by tensoring with a representative…

Let $M$ be a covariant coefficient system for a finite group $G$. In this paper we analyze several topological abelian groups, some of them new, whose homotopy groups are isomorphic to the Bredon-Illman $G$-equivariant homology theory with…

We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all…

The paper gives an answer to the question whether the Galois, separable or etale extension of an Eilenberg-MacLane spectrum in the category of ring spectra is again an Eilenberg-MacLane spectrum. We get a full answer in the Galois case. The…

We define a topological Hochschild (THH) and cyclic (TC) homology theory for differential graded (dg) categories and construct several non-trivial natural transformations from algebraic K-theory to THH(-). In an intermediate step, we prove…

For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of…

We show that the spectrum constructed by Everitt and Turner as a possible Khovanov homotopy type is a product of Eilenberg-MacLane spaces and is thus determined by Khovanov homology. By using the Dold-Thom functor it can therefore be…

The main result of this paper is the computation of TR^n_{\alpha}(F_p;p) for \alpha in R(S^1). These R(S^1)-graded TR-groups are the equivariant homotopy groups naturally associated to the S^1-spectrum THH(F_p), the topological Hochschild…

We generalize the theory of the second invariant cohomology group $H^2_{\rm inv}(G)$ for finite groups $G$, developed in [Da2,Da3,GK], to the case of affine algebraic groups $G$, using the methods of [EG1,EG2,G]. In particular, we show that…

For a finite group $\Gamma$, acting on a finite group $G,$ we find necessary conditions for which the first $\Gamma_0$-equivariant Hochschild cohomology of the group algebra $kG$ is non-trivial, where $k$ is a field of characteristic $p$…

We consider the groups G which arise from real semisimple Jordan algebras via the Tits-Koecher-Kantor construction. Such a G is characterized by the fact that it admits a parabolic subgroup P=LN which is conjugate to its opposite, and for…

We find a simple algebraic model for rational G-equivariant spectra, where G is the p-adic integers, via a series of Quillen equivalences. This model, along with an Adams short exact sequence, will allow us to easily perform constructions…

The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication.…